Modern software systems usually deal with several sorts (types) of data elements simultaneously. Some of these sorts, like integers, booleans, and so on, can be seen as having an immediate, direct nature and therefore are called visible, and they are contrasted with the others, like types of objects (in OO sense), which are called hidden sorts. A language used to specify such software system ha...

In less than a decade, Deduction with Constraints (DwC) has opened a new universe in computer science. DwC can be viewed from two perspectives: one related to the automated deduction framework 17, 19], the other to the development and usage of programming languages based on logic 7, 14]. Within the automated deduction framework, constraints on the generic data structure \terms" have become a po...

Structural synthesis of programs (SSP) is an approach to deductive synthesis of functional programs using types as speciications and based on the Curry-Howard correspondence and on an intensional treatment of the notion of type. The implemented programming environments employing SSP have been based on a fragment of intuitionistic propositional logic (simple type theory) and on a natural-deducti...

We introduce an abstract general notion of system of equations and rewrites between terms, called Term Equational Rewrite System (TERS), and develop a sound logical deduction system, called Term Equational Rewrite Logic (TERL), to reason about equality and rewriting. Further, we give an analysis of algebraic free constructions which together with an internal completeness result may be used to s...

We introduce an abstract general notion of system of equations between terms, called Term Equational System, and develop a sound logical deduction system, called Term Equational Logic, for equational reasoning. Further, we give an analysis of algebraic free constructions that together with an internal completeness result may be used to synthesise complete equational logics. Indeed, as an applic...

About a century ago, Ernst Mach argued that Archimedes’s deduction of the principle of the lever is invalid, since its premises contain the conclusion to be demonstrated. Subsequently, many scholars defended Archimedes, mostly on historical grounds, by raising objections to Mach’s reconstruction of Archimedes’s deduction. In the debate, the Italian philosopher and historian of science Giovanni ...

Deduction modulo is a way to express a theory using computation rules instead of axioms. We present in this paper an extension of deduction modulo, called Polarized deduction modulo, where some rules can only be used at positive occurrences, while others can only be used at negative ones. We show that all theories in propositional calculus can be expressed in this framework and that cuts can al...

Traditional approaches to distributed problem solving have treated the problem as one of distributed search. In this paper, we propose an alternative, logic-based view of distributed problem solving, whereby agents cooperatively solve problems by exchanging information in order to derive the solution to a problem using logical deduction. In particular, we give a knowledge theoretic model of dis...

Game logic is a dynamic modal logic which models strategic two person games; it contains propositional dynamic logic (PDL) as a fragment. We propose an interpretation of game logic based on stochastic effectivity functions. A definition of these functions is proposed, and some algebraic properties of effectivity functions such as congruences are investigated. The relationship to stochastic rela...

Herewith a fairly old concept is published first time and named “Lucas-Interpretation”, which has been implemented in a prototype, which has been proved useful in educational practice and which gains academic relevance with an emerging generation of educational math assistants (EMA) based on Computer Theorem Proving (CTP). Automated Theorem Proving (ATP), i.e. deduction is the appropriate techn...